A certain arithmetic progression has a first term of 10 and a last term of 100.

A certain arithmetic progression has a first term of 10 and a last term of 100. If there are 20 terms in total, what is the common difference?

A certain arithmetic progression has a first term of 10 and a last term of 100. If there are 20 terms in total, what is the common difference?

Step 1: Identify the first term (a) of the arithmetic progression (AP), which is given as 10.
Step 2: Identify the last term of the AP, which is given as 100.
Step 3: Identify the total number of terms (n) in the AP, which is given as 20.
Step 4: Use the formula for the last term of an AP: last term = first term + (number of terms - 1) * common difference.
Step 5: Substitute the known values into the formula: 100 = 10 + (20 - 1) * d.
Step 6: Simplify the equation: 100 = 10 + 19d.
Step 7: Subtract 10 from both sides: 90 = 19d.
Step 8: Divide both sides by 19 to find the common difference (d): d = 90 / 19.
Step 9: Calculate the value of d, which is approximately 4.7368, but since we need a whole number, we round it to 5.

Arithmetic Progression (AP) – An arithmetic progression is a sequence of numbers in which the difference between consecutive terms is constant.
Formula for the nth term of an AP – The nth term of an arithmetic progression can be calculated using the formula: a + (n-1)d, where 'a' is the first term, 'n' is the number of terms, and 'd' is the common difference.